A241625 Smallest number m such that the GCD of the x's that satisfy sigma(x)=m is n.

1, 3, 4, 7, 6, 6187272, 8, 15, 13, 196602, 8105688, 28, 14

Offset

1,2

Comments

This sequence is a sequel to A240667.

Some large known terms: a(16)=2031554, a(25)=1355816, a(31)=8880128, a(80)=11532, a(97)=5488.

a(14) > 10^9. - Michel Marcus, May 09 2014

a(n) is a multiple of A353783(n). Some further terms: a(15) = 497943732, a(17) = 962949708, a(20) = 612372264, a(48) = 12692888, a(53) = 39887316. - Max Alekseyev, Jan 19 2025

Links

Table of n, a(n) for n=1..13.

Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

Formula

For n in A211656, a(n) = sigma(n).

Example

a(2) = 3, because the only x such that sigma(x)=3 is 2.
a(6) = 6187272, because the x's that satisfy sigma(x)=6187272 are [2651676, 2855646] and their GCD is 6.

Prog

(PARI) lista() = {lim = 12000000; nn = 100; out = "a241625.txt"; v = vector(lim, i, sigma(i)); w = vector(lim); for (i=1, lim, vi = v[i]; if (vi <= lim, if (w[vi] == 0, w[vi] = i, w[vi] = concat(w[vi], i)); ); ); for (i=1, nn, got = 0; write1(out, i, " "); for (j=1, #w, wj = w[j]; if (gcd(wj) == i, got = 1; write(out, j); break; ); ); if (! got, write(out, ); ); ); }
(PARI) a(n) = my(m=1); while(gcd(invsigma(m)) != n, m++); m; \\ Michel Marcus, Jan 16 2025; using Max Alekseyev's invphi.gp

Crossrefs

Cf. A000203, A211656, A240667, A353783, A380303, A380304.

Sequence in context: A377378 A344458 A068905 * A081826 A021746 A023849

Adjacent sequences: A241622 A241623 A241624 * A241626 A241627 A241628

Keyword

nonn,more,nice,changed

Author

Michel Marcus, Apr 26 2014

Status

approved